There are possessive adjectives, which fulfil the same function as personal pronouns in the genitive and have gender/number/case markings in many languages.
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CerberusJun 25 '12 at 13:59

It isn't quite what you're looking for but Korean has a notion of "inalienable possessives". So your hat is still your hat even if you aren't wearing it but your hand is [arguably] no longer YOUR hand if it gets chopped off. Hand is an example of an inalienable possession. The interesting part is that in Korean inalienable possessions received the same honourifics as their owner. "Halmeni-uy moca-ga yeybbe-yo" (Grandmother-GEN hat-SUB beautiful) v. "Halmeni-uy son-i yeybbu-sye-yo" (Grandother-GEN hand-SUB beautiful-HON)
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acattleJun 26 '12 at 9:52

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@Cerberus not sure if it's what the questioner is looking for, but I think your comment deserves to be an answer given that many languages have possessive pronouns/adjectives that agree with the possessed object.
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Mark BeadlesJun 26 '12 at 14:35

Thanks to everyone. I am going to accept user1138's answer, being the most upvoted, but all your contributions have been incredibly useful.
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cbrandolinoJun 26 '12 at 20:49

Where did you take your example (glosses) from? Koptjevskaja-Tamm 2000 argues that Romani genitive involves three markers, a marker of the oblique stem ('es' for M.SG, 'a' for F.SG etc.), a genitive marker itself (-k-/-g-), and a marker of gender/case/number agreement with the head (e.g. 'o' for M.SG.NOM).
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Alex B.Jun 27 '12 at 0:08

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The examples are from a Romani grammar outline by Victor Friedman which I used in a class by him seelrc.org:8080/grammar/pdf/romani_bookmarked.pdf As for the glosses, I did them myself based on the glossing standard we used in that class, so they're probably not how other Romani linguistics would gloss them.
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thylacine222Jun 27 '12 at 2:03

Also, "ka"‌ and "ki" are masculine singular and feminine singular; a plural possessed(?) would have "ke". ("us ka ladka" = "his/her boy", "us ki ladki" = "his/her girl", "us ke ladke (ladkiya) = "his/her boys (girls)". So the particle agrees in both gender and number with the possessed. (BTW, although the above comment mentions Sanskrit, note that Sanskrit does not have this feature; in Sanskrit a word in genitive case changes according to the possessor, not the possessed.)
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ShreevatsaRMar 17 '13 at 11:01

In most Grassfields Bantu languages of Cameroon, there is an associative morpheme which agrees with the possessed noun in a genitive construction. In the most minimal type of agreement, the associative marker is a floating low tone for noun classes 1 and 9, and a floating high tone otherwise. Noni, a Beboid language, has eighteen different genitive markers, depending on the noun class of the possessed noun (Hyman 1981: 19).

A mixed case is Nkwen, of the Ngemba group of Grassfields, which has a segmental genitive marker for classes 2, 5, 6 and 19 (agreeing with the possessed), a floating low tone genitive marker for classes 1 and 9, and a floating high tone marker for other classes. (Ncheafor 2002)

Your question doesn't specify whether you are interested just in nouns or also in pronouns or adjectives.

In Spanish these forms of the possessive/genitive adjectives/pronouns (terminology depends on analysis/tradition) are inflected for number, and some also for gender, to agree with the possessed rather than with the possessor: